Intergalactic Travel and Riemann Hypothesis

Immersing (not embedding) the figure-8 Klein bottle in the 3rd dimension + Imaginary time makes the 4th dimension both space and time (since the Klein is 2-dimensional, the statement in the file [in the section BITS AND TOPOLOGY] about a couple of two-dimensional Mobius strips uniting to form a three-dimensional figure-8 Klein bottle needs further explanation) -

A manifold is a collection of points forming a certain kind of set, such as those of a topologically closed surface or an analogue of this in three or more dimensions.

(https://www.bing.com/search?q=meaning+of+manifold&FORM=QSRE7)

A Klein Bottle is a 2-dimensional manifold whose inside is its outside. It can only exist in 4-dimensions! A Klein Bottle cannot be embedded in 3 dimensions, but you can immerse it in 3-D. A photograph of a stapler is a 2-dimensional immersion of a 3-dimensional stapler. (An immersion may have self-intersections; Embeddings have no self-intersections.)

(https://www.kleinbottle.com/whats_a_klein_bottle.htm#:~:text=A%20true%20Klein%20Bottle%20live)

Since the figure-8 Klein bottle referred to in this article can only exist in 4 dimensions, it can be termed a structure of 3 space dimensions which includes the 4th (time) dimension described by Wick rotation. The bottle's immersion in 3 dimensions means its self-intersection allows it to possess only one surface - its inside is its outside (other 3-D objects like wine bottles, for example, have both an inside and an outside). Self-intersection is possible because the 4th dimension of time unites the present with the past and future (explained in the downloaded file) and permits its surface to, in words borrowed from quantum mechanics, occupy more than one location at once i.e. to occupy the position which the bottle's hole would if it were a 3-dimensional object manufactured by the company "Acme Klein Bottle" (mentioned in the website above, "What's a Klein Bottle?") The implied motion from being in more than one place at once is a result of Klein bottles being ultimately composed of the BITS or binary digits of 1 and 0, and switching between those states. These 3+1 dimensions may also be called "an analogue of a topological surface in three or more dimensions".

Of course, the 4th dimension can be thought of as spatial instead of temporal. Mathematically, imaginary time (the text explains why it isn't merely mathematical trickery) is real time which has undergone a Wick rotation. Popularized by Stephen Hawking is the fact that measuring time with imaginary numbers, such as i^2 = -1, makes the distinction between space and time disappear completely (self-intersection by means of a 4th space dimension, rather than the previous paragraph's time, is familiar in topology - but we should remember that both apply in reality since we live in space-time). If a figure-8 Klein bottle is analogous to 3+1 dimensions, what is the reality behind the analogy / similarity / correspondence? All of the information in the universe is contained in two-dimensional packages trillions of times smaller than an atom (in this case, the 2D package is the Mobius Strip) - see Afshordi, N. & Corianò, C. & Delle Rose, L. & Gould, E. & Skenderis, K. From Planck Data to Planck Era: Observational Tests of Holographic Cosmology. Phys. Rev. Lett. 118, 041301. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.04130 (2017).

Therefore, the 3rd dimension (and the distances within it) wouldn't objectively exist but would be the way our perceptions and expectations interpret information contained in the Mobius strip. The implication is that the universe we live in needn't be described as 3 spatial dimensions plus one temporal dimension (3+1 space-time) but, in keeping with the theory of a holographic universe's 3 spatial dimensions being a projection from 2 dimensional information, as 2+1 space-time. Also, using future technology, it should be possible for the time it takes a spacecraft to reach its destination to be the same amount of time as reaching the launchpad from the craft’s position on the launchpad (travel may oneday be instant - the distance to the ship's destination and the time to arrive both equal zero.) If the spacecraft travels through the 4th space dimension, that is equivalent - thanks to imaginary time making the distinction between space and time disappear completely - to taking a trip through time and visiting any point in the past or in the future.

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Using a scientific method that permits arrival at destinations in the universe to occur instantly is not only much more efficient but it avoids dangers like accumulated damage from years of exposure to micrometeorites and cosmic radiation. This article proposes such a method since it's based on an engineering experiment conducted at Yale University and reported in a science journal in 2009. It proposes a mathematical universe - again based on the work of well known scientists but extended into details of my own. A universe that is mathematical in its foundation is required since the gravitational-electromagnetic unification spoken of in connection with the Yale experiment is proposed to function topologically (using the Mobius strip and figure-8 Klein bottle). Admittedly, my proposal is based on technology which has not yet been developed - except for the Yale experiment - but since the first step in developing this technology may already have been taken 13 years ago, determined efforts should see its fulfillment in 50-100 years. And of course, the technology is not limited to travel within the solar system - say, to Jupiter’s moon Europa or to Mars where instant travel would save astronauts and cosmonauts from many months of isolation/threats to muscles and bones/ radiation etc. It could also be used for interstellar and intergalactic exploration, and even for investigations into Earth's past and future if the potential for time travel is realized.

Most people aren’t accustomed to thinking that the universe is literally composed of mathematics (binary digits, Mobius strips, figure-8 Klein bottles, Wick rotation). I developed these ideas after reading about several professors - John Wheeler, Max Tegmark, Erik Verlinde, Ed Fredkin, and Rafael Sorkin. The Introduction will provide understanding that the Riemann hypothesis doesn’t just apply to the distribution of prime numbers but can also apply to the fundamental structure of the mathematical universe’s space-time. When applied to the universe, it explains the static universe, dark matter, dark energy, the Higgs boson/field, and aspects of particle physics like the electroweak interaction.

Unifying gravitation and electromagnetism has this consequence: the electrical-engineering experiment at America's Yale University, together with the ideas of Albert Einstein, tells us how we could travel to other stars and galaxies. An electrical engineering team at Yale demonstrated that, on nanoscales, light can attract and repel itself like electric charges or magnets.

“Tunable bipolar optical interactions between guided lightwaves” by Mo Li, W. H. P. Pernice & H. X. Tang, Nature Photonics 3, 464 – 468 (2009)

This is the Optical Bonding Force. For 30 years until his death in 1955, Einstein worked on his Unified Field Theory with the aim of uniting electromagnetism (light is one form of this) and gravitation. Achievement of this means the quantum components (gravitons) of gravity/spacetime-warps between spaceships and stars could mimic the Optical Force and be attracted together, thereby eliminating distance (this, possibly acting in partnership with repulsion, could produce a wormhole, or shortcut between folds in space and time). If the gravitons are superposed and entangled, distances between both points in space and points in time are totally eliminated.